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GCF of 98/214, 38/130

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 98/214, 38/130 i.e 2/13910 easily. The following is the detailed procedure to determine the greatest common factor of fractions 98/214, 38/130.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 98/214,38/130?

Given fractions are 98/214,38/130

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 98/214,38/130, numerators are 98,38

Denominators are 214,130

The GCF of 98,38 is 2 .

LCM of 214,130 is 13910.

The greatest common factor of 98/214,38/130 = [GCF of 98,38]/[LCM of 214,130]= 2/13910

Therefore, the GCF of 98/214,38/130 is 2/13910.

Greatest Common Factor of 98,38

To find the highest common factor of 98,38, we have to find the factors of both numbers and list the highest common factor.

The factors of 98 are 1, 2, 7, 14, 49, 98

The factors of 38 are 1, 2, 19, 38

The HCF of 98,38 is 2.

Lets's calculate GCF of 98,38

Greatest Common Factor (GCF) of 98,38 By Common Division

2 98, 38
49, 19

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 98,38 By Matching Biggest Common Factor Method

Greatest Common Factor of 98,38 By Matching Biggest Common Factor Method

Now, list down the factors of 98

:

1,2,7,14,49,98

Now, list down the factors of 38

:

1,2,19,38

Greatest Common Factor

We found the factors 98,38 . The biggest common factor number is the GCF number.
So the greatest common factor 98,38 is 2.

Lets's calculate LCM of 214,130

Lowest Common Multiple of 214,130 using Common Division

2 214, 130
107, 65

∴ So the LCM of the given numbers is 2 x 107 x 65 = 13910

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/13910

Therefore, the GCF of Fractions 98/214,38/130 is 2/13910

Least Common Multiple of 214,130 with GCF Formula

Least Common Multiple of 214,130 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 214,130 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,130) = 2

common factors(in case of two or more numbers have common factors) = 1

GCF(214,130) x common factors =2 x 1 = 2

LCM(214,130) = ( 214 × 130 ) / 2

LCM(214,130) = 27820 / 2

LCM(214,130) = 13910


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FAQs on GCF of Fractions of 98/214, 38/130

1. What is the HCF of 98,38?

The HCF of 98,38 is 2

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 98/214, 38/130?

Answer: GCF of Numerators as per given numbers 98/214, 38/130 is

GCF of Numerators i.e. for 98,38 is 2

LCM of denominators i.e. for 214,130 is 13910.

Thus, GCF of Fractions is 2/13910.Finally, GCF of Fractions for 98/214, 38/130 is 2/13910.